Multiplying Square Roots and Multiplying Radicals Explained

Learn How to Multiply Radicals and How to Multiply Square Roots in 3 Easy Steps (Free Worksheet Included)

Learn How to Multiply Radicals (and How to Multiply Square Roots) in 3 Easy Steps

Before you learn how to multiply radicals and how to multiply square roots, you need to make sure that you are familiar with the following vocabulary terms:

Radical vs. Radicand

The radical is the square root symbol and the radicand is the value inside of the radical symbol. The radicand can include numbers, variables, or both.

The Multiplication Property of Square Roots

The key to learning how to multiply radicals is understanding the multiplication property of square roots.

The property states that whenever you are multiplying radicals together, you take the product of the radicands and place them under one single radical.

For example, radical 5 times radical 3 is equal to radical 15 (because 5 times 3 equals 15).

How to Multiply Radicals and How to Multiply Square Roots Example

Now let’s take a look at an example of how to multiply radicals and how to multiply square roots in 3 easy steps.

Problem:

Step One: Simplify the Square Roots (if possible)

In this example, radical 3 and radical 15 can not be simplified, so we can leave them as they are for now.

Step Two: Multiply the Radicands Together

Now you can apply the multiplication property of square roots and multiply the radicands together. In this case, radical 3 times radical 15 is equal to radical 45 (because 3 times 15 equals 45).

Step Three: Simplify the Result (if possible)

The third and final step is to simplify the result if possible.

Can radical 45 be simplified?

The answer is yes.

Since radical 45 is equal to radical 9 times radical 5, and because radical 9 is equal to 3 (since 9 is a perfect square), we can simplify radical 45 to 3 times radical 5 (see the diagram below for a more detailed look on how to simplify square roots).

Finally, we can conclude that the final answer is:

Looking for more sample problems? Check out the free video lesson below to learn more about how to multiply radicals and how to multiply square roots :

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How to Multiply Radicals and How to Multiply Square Roots Worksheet (with Answer Key)

Are you looking to get some more practice with multiplying radicals, multiplying square roots, simplifying radicals, and simplifying square roots?

Click the link below to access your free practice worksheet from Kuta Software:

Free Multiplying Radicals Worksheet

Share your ideas, questions, and comments below!

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By Anthony Persico

Anthony is the content crafter and head educator for YouTube's MashUp Math . You can often find me happily developing animated math lessons to share on my YouTube channel . Or spending way too much time at the gym or playing on my phone.

Negative Exponent Rule Explained in 3 Easy Steps

Understanding the Negative Exponent Rule

Before you learn to understand and apply the Negative Exponent Rule, let’s recap what you already know about positive exponents.

For example, 5^2, or 5 squared, is equal to 5x5, or 25.

But what would change if the exponent (2 in this case) was negative instead of positive?

In math, when you think of the word negative or negate, the implication is that you must perform the opposite or inverse operation.

With positive exponents, you perform multiplication.

So, with negative exponents, you perform the opposite or inverse of multiplication, which is…

Division (because division is the inverse operation of multiplication).

Now you are ready to use the Negative Exponent Rule

Negative Exponent Rule in 3 Easy Steps

Now let’s look at the previous example again, except this time the exponent is -2 (negative two).

Step One: Rewrite the Value with Negative Exponent as a Fraction

Since we are performing division (the inverse of multiplication), we will rewrite the value as a fraction with a numerator of one.

Step Two: Trash the Negative Sign and Move the Value to the Denominator

To complete the fraction, get rid of the negative sign in front of the exponent and move the remaining value (5 squared) to the denominator of the fraction.

Notice that 5 to the negative second power is equal to one over 5 to the positive second power.

via GIPHY

Step Three: Trash the Negative Sign and Move the Value to the Denominator

The final step is to simplify rewriting 5 squared as 25 and concluding that 5^-2 is equal to 1/25 or 0.04.

Expressed as a fraction.

Expressed as a decimal.

Looking for a visual representation of how the negative exponent rule works?

Check out the free video lesson below to learn more about how the negative exponent rule.

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Free Negative Exponents Worksheet

This lesson includes a free Negative Exponent Rule worksheet that accompanies the video lesson. Click the link below to get yours!

Download your free Negative Exponents Worksheet Lesson Guide PDF

Share your ideas, questions, and comments below!

(Never miss a Mashup Math blog--click here to get our weekly newsletter!)

By Anthony Persico

Anthony is the content crafter and head educator for YouTube's MashUp Math . You can often find me happily developing animated math lessons to share on my YouTube channel . Or spending way too much time at the gym or playing on my phone.

Celebrate National Chocolate Cupcake Day with These Free Math Puzzles

Celebrate National Chocolate Cupcake Day in Your Math Classroom with These Free Math Puzzles

Did you know that October 18th is National Chocolate Cupcake Day in the United States?

You can celebrate at home by baking up a batch of yummy chocolate cupcakes to share with family, friends, and co-workers!

And you can celebrate in your classroom with two fun math cupcake-themed math puzzles for students in grades 3-8!

The first Cupcake Day Challenge is a Multiplication Table Puzzle.

The second Cupcake Day Challenge is an Area Model Puzzle.

These activities are perfect for warm-up and cool-down activities as well as for supplementing your lesson plans, extra credit assignments, and homework.

1.) Chocolate Cupcake Day Multiplication Puzzle

This puzzle challenges students to use their math and reasoning skills to find the value of 6 different symbols contained within a multiplication table (it works like a bingo-table where the icon in each box represents the product of its corresponding column and row.)

*Keep reading to get the answer key.

2.) Chocolate Cupcake Day Area Model Puzzle

This puzzle challenges students to apply their understanding of multiplication to find the missing values in an area model that represents the products of two different numbers.

*Keep reading to get the answer key.

These puzzles are samples from my best-selling workbook 101 Math Challenges for Engaging Your Students in Grades 3-8.

The book is available as a PDF download and you can also get a hard copy on Amazon (Free Amazon Prime Shipping Included; pages are in black-and-white).

And here are the solutions to today's puzzles:
Multiplication Table Answer Key:

Area Model Answer Key:

Plain Cupcake=20, Sprinkle Cupcake=80, Chocolate Bar=5, Milk=4, Baker=100

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Math Video Games Puzzles for Grades 1-6: Are Your Kids Ready?

Are Your Students Ready for Some Super Fun Video Games-Themed Math Puzzles?

Kids love playing video games. 

Whether it's on X-Box, Nintendo Switch, or a Smart Phone, your students are likely enjoying playing some sort of video game in their free time.

Sharing your enthusiasm for video games is a great way to build relationships with your kids—plus you can channel that enthusiasm towards math learning activities!

So go ahead and share today's video game-themed math puzzles with your kiddos! It makes for a great warm-up or cool-down activity to get your kids to practice applying logic, reasoning, and order of operations.

Why? Because kids love fun (and 100% free) math puzzles!

The following video game-themed math puzzles for elementary and middle school students are samples from my best-selling PDF math workbook: The Big Book of Super Fun Math Puzzles for Grades 1-6.

The puzzles are tiered by difficulty using the following color system used in the book.

Pink Level (Grades 1-2) | Blue Level (Grades 3-4) | Green Level (Grades 5-6+)

Free Video Games Math Puzzles for Grades 1-6+

(answer keys to follow)

Pink Level Puzzle ( for Grades 1-2)

Free Math Resources: Astronomy Day Math Puzzles for Grades 1-6

Blue Level Puzzle (for Grades 3-4)

Free Math Resources: Pet-Themed Math Puzzles for Grades 1-6

Green Level Puzzle (for Grades 5-6+)

Wait! Do You Want More Fun Math Puzzles to Share with Your Kids??

If you and your students like these pet-themed puzzles, then you should definitely get yourself a copy of the new book, which shares over 300 kid-friendly, differentiated, and printable math puzzles and activities!

It covers differentiated topics including:
-addition and subtraction
-multiplication and division
-order of operations
-inverse operations
-adding and subtracting fractions
-multiplication tables
-area models
-math writing activities

And the book includes a really cool Make Your Own Math Puzzle hands-on activity requiring only scissors and glue to complete. 

It also includes a complete answer key and several useful templates.

Take a Look Inside

You can access the entire Table of Contents by clicking here.

And you can click the links below to access some sample pages:

Pink Level Samples (for Grades 1 and 2): Sample A | Sample B

Blue Level Samples (for Grades 3 and 4): Sample A | Sample B | Sample C

Green Level Samples (for Grades 5 and 6+): Sample A | Sample B | Sample C

There are three puzzles per page and they include the familiar name/date/directions sections that are included in typical math worksheets, which makes them easier to print and share aswarm-up and exit-ticket activities, in lesson plans, and as extra credit and homework assignments.

Click here to get your copy of The Big Book of Super Fun Math Puzzles for Grades 1-6.

And check out the solutions to the pet-themed puzzles below:

Pink Level (Grades 1-2): Nintendo Switch=3, Pacman=10, Gameboy=5, ?=8

Blue Level (Grades 3-4): Nintendo Switch=11, Pacman=11, Gameboy=9, X-Box Controller=16, ?=176

Green Level (Grades 5-6+): Nintendo Switch=6, Pacman=6, Gameboy=17, X-Box Controller=76, ?=224

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Sharing video game math challenges and puzzles with your students is just one effective strategy for boosting engagement in your classroom. Subscribe to our mailing list here to get more free daily resources, lesson plans, ideas, and insights for K-12 math teachers in your inbox every week.

Read More Posts About Math Education:

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By Anthony Persico

Anthony is the lead educator and founder of Mashup Math. He lives in Denver, Colorado and is also a YouTube for Education partner. Follow him on Twitter at @mashupmath.

Teacher Burnout Is Real. Here Are 3 Effective Prevention Strategies

These Effective Strategies Will Help You to Maintain a Healthier Work-Life Balance and Prevent Teacher Burnout

A Post By: Anthony Persico

The demands of being a classroom teacher can be extremely stressful and often lead to burnout. These strategies and helpful reminders can help you achieve work-life balance and learn to manage teaching-related stress in healthy ways.

Edutopia describes teacher burnout as a state of continuous stress that leads to detachment and cynicism, exhaustion (both physical and emotional), and feeling ineffective and unaccomplished. It can also be described as depression caused by the workload involved with being a teacher.

When teachers fail to prioritize a healthy work-life balance, they put themselves at risk of burning out and losing their passion for being an educator. In fact, teacher burnout may be a leading factor in why 44% of new teachers quit the profession within their first five years.

However, there are many effective strategies that teachers can use to establish healthy boundaries between work and personal life, prevent themselves from being overextended and overstressed, and get through an entire school year without burning out.

3 Effective Strategies for Preventing Teacher Burnout

1.) Learn to Say No

Teachers often make more commitments than they can reasonably handle. While your heart is probably in the right place, you place yourself on the fast track to burnout when you say ‘yes’ too often.

In fact, once you establish yourself as someone who never says ‘no’, students, parents and administrators will only ask more of you, as they are skilled at squeezing every drop of energy a teacher has to offer.

But you have the right to say 'no' to unreasonable requests —without feeling guilty. In the long run, your students and your school will be better off having teachers who live healthy and balanced lives (rather than ones who are exhausted and burnt out).

Read More: Why Every Teacher Should Learn to Say 'No'

2.) Make Time for Yourself

Many teachers make the mistake of spending too much of their personal time working on school-related tasks. This imbalance can easily lead to feeling burnt out way before the school year has ended.

Establishing clear and firm boundaries between your work and personal life is a key element to establishing balance. Some ideas for setting boundaries include:

• No checking emails after the school day has ended.

• No grading or lesson planning on Fridays and Saturdays.

• Staying after school for extra help only two days per week.

• No committing to extracurricular activities.

In addition to setting boundaries, be sure to include non-negotiable personal time in your schedule for things like exercise, reading, and spending time with friends and loved ones.

Read More: A Message to New Teachers: Failure, Feedback, and Focus

3.) Practice Mindfulness

The everyday demands of teaching can be stressful and overwhelming. By practicing mindfulness through meditation, you can effectively learn to slow yourself down, maintain perspective, and deal with stress in a healthy way.

Mindfulness—a set of skills that allows one to be calm and focused on the present moment—can be a real game-changer for teachers looking to manage stress and avoid teacher burn out. Even a few minutes of practice each day can make a big difference.

The following infographic from Harvard Graduate School of Education shares more information on how teachers can use mindfulness to increase well-being, and overcome challenges.

Read More: 21 Time-Saving Strategies, Activities, and Ideas All Math Teachers Should Know

Building Mindfulness For Teachers Guide Learn more about early childhood education from Professional Education at the Harvard Graduate School of Education

Did you find this post on preventing teacher burnout helpful?

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Anthony is the lead educator and founder of Mashup Math. He lives in Denver, Colorado and is also a YouTube for Education partner. Follow him on Twitter at @mashupmath.

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